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In one-dimensional systems a twisted superfluid phase is found which isinduced by a spontaneous breaking of the time-reversal symmetry. Using thedensity-matrix renormalization group allows us to show that the excitationenergy gap closes exponentially causing a quasi-degenerate ground state. Thetwo degenerate ground states are connected by the time-reversal symmetry whichmanifests itself in an alternating complex phase of the long-range correlationfunction. The quantum phase transition to the twisted superfluid is driven bypair tunneling processes in an extended Bose-Hubbard model. The phaseboundaries of several other phases are discussed including a supersolid, a pairsuperfluid, and a pair supersolid phase as well as a highly unconventional Mottinsulator with a degenerate ground state and a staggered pair correlationfunction.

Twisted superfluid phase in the extended one-dimensional Bose-Hubbard model